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A061395
Let p be the largest prime factor of n; if p is the k-th prime then set a(n) = k; a(1) = 0 by convention.
405
0, 1, 2, 1, 3, 2, 4, 1, 2, 3, 5, 2, 6, 4, 3, 1, 7, 2, 8, 3, 4, 5, 9, 2, 3, 6, 2, 4, 10, 3, 11, 1, 5, 7, 4, 2, 12, 8, 6, 3, 13, 4, 14, 5, 3, 9, 15, 2, 4, 3, 7, 6, 16, 2, 5, 4, 8, 10, 17, 3, 18, 11, 4, 1, 6, 5, 19, 7, 9, 4, 20, 2, 21, 12, 3, 8, 5, 6, 22, 3, 2, 13, 23, 4, 7, 14, 10, 5, 24, 3, 6, 9, 11, 15
OFFSET
1,3
COMMENTS
Records occur at the primes. - Robert G. Wilson v, Dec 30 2007
For n > 1: length of n-th row in A067255. - Reinhard Zumkeller, Jun 11 2013
a(n) = the largest part of the partition having Heinz number n. We define the Heinz number of a partition p = [p_1, p_2, ..., p_r] as Product(p_j-th prime, j=1...r) (concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). For example, for the partition [1, 1, 2, 4, 10] we get 2*2*3*7*29 = 2436. Example: a(20) = 3; indeed, the partition having Heinz number 20 = 2*2*5 is [1,1,3]. - Emeric Deutsch, Jun 04 2015
FORMULA
A000040(a(n)) = A006530(n); a(n) = A049084(A006530(n)). - Reinhard Zumkeller, May 22 2003
A243055(n) = a(n) - A055396(n). - Antti Karttunen, Mar 07 2017
a(n) = A000720(A006530(n)). - Alois P. Heinz, Mar 05 2020
EXAMPLE
a(20) = 3 since the largest prime factor of 20 is 5, which is the 3rd prime.
MAPLE
with(numtheory):
a:= n-> pi(max(1, factorset(n)[])):
seq(a(n), n=1..100); # Alois P. Heinz, Aug 03 2013
MATHEMATICA
Insert[Table[PrimePi[FactorInteger[n][[ -1]][[1]]], {n, 2, 120}], 0, 1] (* Stefan Steinerberger, Apr 11 2006 *)
f[n_] := PrimePi[ FactorInteger@n][[ -1, 1]]; Array[f, 94] (* Robert G. Wilson v, Dec 30 2007 *)
PROG
(PARI) a(n) = if (n==1, 0, primepi(vecmax(factor(n)[, 1]))); \\ Michel Marcus, Nov 14 2022
(Haskell)
a061395 = a049084 . a006530 -- Reinhard Zumkeller, Jun 11 2013
(Python)
from sympy import primepi, primefactors
def a(n): return 0 if n==1 else primepi(primefactors(n)[-1])
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, May 14 2017
CROSSREFS
KEYWORD
easy,nice,nonn
AUTHOR
Henry Bottomley, Apr 30 2001
EXTENSIONS
Definition reworded by N. J. A. Sloane, Jul 01 2008
STATUS
approved